Chapter 32, Problem 72GP

A slab of thickness D, whose two faces are parallel, has index of refraction n. A ray of light incident from air onto one face of the slab at incident angle θ₁ splits into two rays A and B. Ray A reflects directly back into the air, while B travels a total distance ℓ within the slab before reemerging from the slab’s face a distance d from its point of entry (Fig. 32–60). (a) Derive expressions for ℓ and d in terms of D, n, and θ₁. (b) For normal incidence (i.e., ${\theta }_1=0°$) show that your expressions yield the expected values for ℓ and d.